提出新型回归鲁棒性认证框架，利用梯度信息提升认证精度。
Higher-Order Certified Robustness for Regression
- 基于预测中心的认证机制，融合均值、方差与梯度信息
- 在MNIST旋转任务中，认证范围比当前最优方法提升显著
- 适用于对模型输出稳定性要求高的回归场景
随机平滑已成为分类器对抗鲁棒性认证的可扩展方法，但其在回归任务中的应用仍不充分，且面临独特挑战。现有回归认证依赖概率接受区域，未能利用函数的局部几何特性。本文提出一种新型认证框架，构建以预测为中心的鲁棒性保证，确保平滑模型预测的稳定性，并实现测试时的实用可计算性。通过显式引入均值、方差和梯度，探索多种证书构造方式。特别地，在MNIST旋转任务中，利用梯度信息的方法相比当前最优的alpha平滑法，获得显著更紧的鲁棒性证书。
原文摘要 · Abstract (English)
Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model's prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular, we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, alpha-smoothing.
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